President Obama on Tuesday rejected calls for a short-term increase in the legal limit on government borrowing and summoned congressional leaders to the White House to restart negotiations over a long-term plan to restrain the deepening national debt.

With an Aug. 2 deadline closing in, Obama urged lawmakers in both parties to break the stalemate that halted talks nearly two weeks ago and seize what he called “a unique opportunity to do something big” to rebalance the nation’s finances.

“There may be some in Congress who want to do just enough to make sure that America avoids defaulting on our debt in the short term but then want to kick the can down the road when it comes to solving the larger problem of our deficit. I don’t share that view,” Obama told reporters during a late-afternoon appearance at the White House.

With the surprise announcement, Obama sought to take charge of a situation that was rapidly devolving into a dangerous game of chicken: Republicans have refused to discuss any debt-reduction deal that includes higher taxes, while Democrats have rejected any deal based solely on spending cuts.

The president also struck a more conciliatory tone than he did in a news conference last week, when he ridiculed Republicans’ work ethic and accused them of seeking to prevent the super-rich from making sacri­fices alongside those who stand to suffer from unprecedented cuts to federal programs.

Obama said he “made progress” in talks with congressional leaders over the Fourth of July weekend. He met with House Speaker John A. Boehner (R-Ohio) on Sunday at the White House. On Tuesday, the president invited the top two leaders from each party in the House and Senate to come to the White House on Thursday to “drive towards a final agreement.”

“It’s my hope that everybody is going to leave their ultimatums at the door,” he said.

Polls show that Americans largely disapprove of Obama’s handling of the economy, and failing to reach a debt-reduction deal could make the president more vulnerable leading into the 2012 election.

Republicans reacted warily to the creation of a new negotiating structure and to Obama’s suggestion that the parties produce the biggest debt-reduction package of the past two decades over the next two weeks. They said they would attend the Thursday summit but offered little hope for progress as long as higher taxes are on the table.

“We’re not dealing just with talking points about corporate jets or other ‘loopholes.’ The legislation the President has asked for — which would increase taxes on small businesses and destroy more American jobs — cannot pass the House, as I have stated repeatedly,” Boehner said in a statement. “I’m happy to discuss these issues at the White House, but such discussions will be fruitless until the President recognizes economic and legislative reality.”

The battle over the debt limit, which has dominated debate in Washington for much of the spring, is set to intensify to code-red levels. Treasury Secretary Timothy F. Geithner has said he will run out of money to pay the nation’s bills — forcing the first government default in U.S. history — unless Congress acts to increase the $14.3 trillion limit by Aug. 2. The Treasury needs a little more than $2 trillion in fresh borrowing authority to cover the government’s needs through the 2012 election.

Republicans, however, are refusing to raise the debt ceiling unless the increase is accompanied by spending cuts of an equal amount. In bipartisan talks led by Vice President Biden, negotiators had identified more than $1 trillion in savings before Republicans pulled the plug on June 23, declaring an impasse over the issue of taxes.

On Tuesday, a GOP aide familiar with the talks put the numbers even higher, saying the two sides had agreed on as much as $2.3 trillion in potential savings, including more than $300 billion in interest payments averted through lower borrowing. That would match the amount needed to cut a long-term deal.

But serious hurdles block the path forward. Republicans, for example, have refused to agree to Democratic demands for a “firewall” between defense and non-defense spending that would distribute the pain broadly across government, hitting the military as well as domestic agencies. And while Democrats have offered to reduce spending on government health programs as long as the reductions do not affect benefits, Republicans have been adamantly opposed even to eliminating tax breaks that are unpopular among Republicans.

Since the talks broke down, some lawmakers in both parties have expressed doubts about their ability to negotiate, draft and approve such a momentous package of spending cuts and revenue increases in the dwindling time that remains. That has fueled talk of a short-term extension of the debt limit that would permit the Treasury to cover the bills for a few more months while discussions continue.

On Sunday, Sen. John Cornyn (R-Tex.) issued the latest call for a “mini-deal.” Cornyn, who is in charge of 2012 Republican Senate campaign strategy, said, “We’ll take the savings we can get now, and we will re-litigate this as we get closer to the election.”

Many lawmakers are loathe to defer a decision on the debt until next year, however, because that would force them to take another unpopular vote to raise the debt limit within months of facing voters. Such a vote could prove devastating to as many as a dozen vulnerable Senate Democrats, and Senate Minority Leader Mitch McConnell (R-Ky.), who stands to gain control of the Senate in the 2012 elections, has been perhaps the most persistent advocate of a short-term deal.

House Republicans would also be vulnerable, and Boehner has said he wants a long-term deal.

Obama weighed in Tuesday, noting that a remarkable bipartisan consensus has emerged about the scope and severity of the nation’s debt problem. “Most of us already agree that to truly solve our deficit problem, we need to find trillions in savings over the next decade, and significantly more in the decades that follow,” he said. “And that’s the kind of substantial progress that we should be aiming for here.”

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